5.2.2. Sequencing and routing for man-on-board AS/RS
The routing problem for man-on-board AS/RS is
a TSP with a Chebyshev distance metric. The literature
on this problem has been focused primarily on
efficient heuristics. Gudehus (1973) describes the
band heuristic, which divides the rack into two
equal height horizontal bands; the points in the
lower band are visited in the increasing x-coordinate
direction, while the points in the upper band are visited
in the opposite direction. If the tour must visit
many points, the rack may be divided into several
pairs of horizontal bands. Goetschalckx and Ratliff
(1988c) propose a convex hull algorithm based on
the property of Chebyshev metric that some points
not on the convex hull can be inserted into it without
incurring additional travel distance. The algorithm
constructs the convex hull of all the picking
locations, then those free insertion locations for
each segment of the convex hull are identified and
inserted into the convex hull, and then the remaining
points are sequentially inserted into the tour in
a way that minimizes the increase in tour length
for each insertion. The band algorithm is easy to
implement and computationally efficient, but might
give inferior solutions in some cases. On the other
hand, the convex hull algorithm is effective in finding
short tours, but is difficult to implement (to find